Selection above the baseline:
quantifying the advection effect in four domains of cumulative culture



Andres Karjus



Centre for Language Evolution, University of Edinburgh
& University of Tartu

a.karjus@sms.ed.ac.uk | andreskarjus.github.io | @AndresKarjus

Language and culture dynamics

Why and how does language (~culture in general) change over time?

Diachronic corpora

Topics in a corpus of language

The topical-cultural advection model

How does this work?

How well does it work?

Cultural evolution

The data

Residuals

-Top positive residuals (~selection): celery root, sauerkraut, baking powder, granulated sugar, pork fat, corn starch

-Top negative: powder sugar, powdered loaf sugar, pearl ash (potassium carbonate), sauce, lemon juice, tomata

Some more culinary explorations

Ingredient network: potential interactions

Red: new ingredients (size = log frequency increase). Gray: old ingredients. Links: width indicates cosine similarity.

Some basic network analysis

degree(new ingredients) ~ advection(new ingr); R^2=0.31

degree(new ingredients) ~ advection(new ingr) * mean(degrees(old ingr neighbors)); R^2=0.4

Conclusions









Extras

Parameters

Math

The advection value of a word in time period \(t\) is defined as the weighted mean of the changes in frequencies (compared to the previous period) of those associated words. More precisely, the topical advection value for a word \(\omega\) at time period \(t\) is

\[\begin{equation} {\rm advection}(\omega;t) := {\rm weightedMean}\big( \{ {\rm logChange}(N_i;t) \mid i=1,...m \}, \, W \big) \end{equation}\]

where \(N\) is the set of \(m\) words associated with the target at time \(t\) and \(W\) is the set of weights (to be defined below) corresponding to those words. The weighted mean is simply

\[\begin{equation} {\rm weightedMean}(X, W) := \frac{\sum x_i w_i }{\sum w_i} \end{equation}\]

where \(x_i\) and \(w_i\) are the \(i^{\rm th}\) elements of the sets \(X\) and \(W\) respectively. The log change for period \(t\) for each of the associated words \(\omega'\) is given by the change in the logarithm of its frequencies from the previous to the current period. That is,

\[\begin{equation} {\rm logChange}(\omega';t) := \log[f(\omega';t)+1] - \log[f(\omega';t-1)+1] \end{equation}\]

where \(f(\omega';t)\) is the number of occurrences of word \(\omega'\) in the time period \(t\). Note we add \(1\) to these frequency counts, to avoid \(\log(0)\) appearing in the expression.

Ingredient cosine similarities

Based on ingredient co-occurrence in the cookbooks. Displaying only the igredients with at least one neighbor >0.6 similarity (corresponds to edge width) and excluding nodes with weaker similarity links. Color corresponds to log frequency change (red=increase).




*This research was supported by the scholarship program Kristjan Jaak, funded and managed by the Archimedes Foundation in collaboration with the Ministry of Education and Research of Estonia.